The ever increasing requirements on electroacoustic transducers, meaning increased sound pressure and sound quality at a decreased size of said transducers, lead to certain problems, wherein the membrane, which is a very important part, represents one of them. For good sound reproduction, on the one hand, a low resonant frequency of the membrane should be obtained, which means that thin membranes made of soft materials should be chosen. High sound pressures, on the other hand, demand relatively thick and stiff membranes. So there are opposite basic requirements for a membrane, which are to be balanced and which define a limit to what is technically possible. Nowadays transducers using membranes made of common materials such as Polycarbonate (PC), Polyetherimide (PEI), Polyethylenterephthalate (PET), or Polyethylennaphtalate (PEN), have reached this borderline, which is to be broken through.
To explain the aforesaid problems in more detail, reference is now made to FIG. 1, which shows a simplified cross section of a speaker 1. The speaker 1 comprises a membrane 2, a coil 3 attached to said membrane 2, a magnetic system 4 interacting with the coil 3, and a housing 5, which keeps the aforesaid parts together. The membrane 2 has a certain thickness d and together with housing 5 forms a back volume Vb. Membrane 2 normally also comprises corrugations, which enable its movement, which corrugations are left in this and further drawings for the sake of brevity.
FIG. 2 now shows the movement of the membrane 2. Membrane 2 may move in the direction of movement MOV. Thin lines indicate its lower dead center and its upper dead center. The distance of movement s of the membrane 2 is measured in direction of movement MOV, wherein a positive distance of movement s indicates an upward movement, a negative one a downward movement.
FIG. 3 shows differential operating loads dFo acting on the membrane 2. The coil 3, which is not shown, forces the membrane 2 to move up and down. Integration of all differential operating loads dFo results in an overall operating load Fo, which is to be produced by the magnetic force between coil 3 and magnetic system 4. Loads F directed upwards are positive, those directed downwards are negative.
FIG. 4 shows a differential part 2dp of membrane 2 (see also dotted circle in FIG. 3). As it has a differential mass dm, an acceleration—a downwards causes a differential accelerating force dFa to go up:dFa=a·dm=ω2·smax·dm=2·π·f2·smax·dm 
wherein ω is angular velocity and f is the frequency of the membrane 2 and wherein smax is the maximum amplitude of the membrane 2. At the same time a differential pressure force dFp is acting on the differential part 2dp, since it is assumed that the membrane 2 is below its idle position in FIG. 4. Thus the back volume Vb is compressed, causing a positive pressure force dFp acting perpendicularly on the membrane 2 according to the adiabatic gas equationp·Vκ=const
wherein p is a pressure, V is a volume and K is the adiabatic coefficient (for air under standard conditions κ=1.402). Hence an increase of the volume V leads to a decrease of the pressure p and vice versa. Therefore, the pressure p in the back volume Vb decreases when the membrane 2 moves upwards. The differential pressure force dFp may now be calculated as follows
      ⅆ          F      p        =            p      ·              ⅆ                                  ⁢        A              =                  p        0            ·                        (                                    Vb              0                        Vb                    )                κ            ·              ⅆ                                  ⁢        A            
wherein dA is a differential area of the differential part 2dp, Vb0 and p0 are the back volume of the transducer 1 and the pressure therein at the membrane's idle position.
Both, the differential accelerating force dFa and the differential pressure force dFp form the differential operating load dFo. The latter one causes the membrane 2 to be bent. The elasticity of the membrane, defined by the Young's modulus E of the membrane 2, transversal to its extension of thickness d, acts against this bending (see also Eavg in FIG. 7 for the definition of said direction). Hence a certain operating load Fo leads to a certain movement of the membrane 2.
FIG. 5 now shows the distance of movement s of the membrane 2 as well as the differential loads dF acting on the membrane 2 over time. It is assumed that a sinusoidal current flows through the coil 3. Hence the membrane 2 moves sinusoidally as well, visualized by the graph for the distance of movement s (solid thin line). The differential accelerating force dFa (dash-and-dot line) is sinusoidal as well, as it is directed opposite to the acceleration a, which is the second derivation of the distance of movement s. In contrast to that is the differential pressure force dFp (dashed line), which is at its negative maximum in the upper dead center of the membrane 2. Both the differential accelerating force dFa and the differential pressure force dFp forms the differential operating load dFo (solid bold line) as stated before. Since membranes in general are relatively lightweight and sound pressure is relatively high (meaning that the amplitude of the membrane's movement is also high), the differential pressure force dFp is higher than the differential accelerating force dFa. Since both are in phase, the differential operating load dFo shows an in-phase negative sinusoidal graph. The same applies to overall loads, meaning that the differential loads may be integrated over the whole membrane 2 or at least over part of said membrane 2.
FIG. 6 now shows the membrane 2 in its idle position as well as in its upper dead center (thin dashed line). As long as the operating load Fo is below a so-called critical buckling/crinkling load Fbc, the dome of the membrane 2, which is the part of the membrane 2 inside the coil 3, substantially keeps its shape. At the least it is bent outwards. When the operating load Fo exceeds the critical buckling/crinkling load Fbc, the dome of the membrane 2 snaps inwards due to the so-called buckling and/or crinkling effect (thin solid line).
The same applies to the border area of the membrane 2 outside the coil 3 as well. Normally it is bent outwards, but at a certain load it may snap inwards. This effect is quite complex and highly depends on the shape of the membrane 2. A higher dome for instance would buckle much later than a flat one. Corrugations too, which are normally part of a membrane but which were left out for the sake of brevity here, highly influence this buckling and/or crinkling. Thus this effect may also be limited to a relatively small area of the membrane 2, for example if there are sharp edges or intersections, which essentially influence the mechanical behavior of the membrane 2. Because of the complexity of the buckling/crinkling effect, it is only possible to calculate where and when buckling/crinkling occurs by the use of computer simulation using the finite elements method.
In any case the aforesaid buckling and/or crinkling is an unwanted effect because it dramatically draws down the acoustic quality of a transducer as can easily be imagined. Membrane 2 is to compress the air in front of the transducer in its upper position, whereas it more or less decompresses the air, when the membrane 2 buckles. So the sound wave does not show a sinusoidal graph anymore, although the current in the coil 3 does. This is unacceptable for present-day requirements.
To explain the balancing problem of sound quality and sound pressure, which was briefly mentioned in the first paragraph of the “background of the invention” in more detail, reference is now made to basic formulas for the resonant frequency and for the stiffness of a membrane (meaning its resistance against movement in direction of movement or its spring constant):fres=k1·d·√{square root over (E)}
According to the first formula the resonant frequency fres of a membrane depends on a first form factor k1, the thickness d of the membrane and the Young's modulus E of the membrane. Since there is a tendency to decrease the resonant frequency fres, so as to increase the acoustic performance of a transducer, there is also a tendency to reduce the thickness d of the membranes. This leads to a drawback as the stiffness S of a membrane in its direction of movement is proportional to the square of the resonant frequency.S∝fres2=k12·d2·E 
It can easily be seen that a reduction of the thickness d and thus a reduction of resonant frequency fres results in a decrease of the stiffness S. A lower stiffness S in turn results in a decreased maximum possible sound pressure and an increased tendency for buckling/crinkling, which is undesired. So one could try to increase the Young's modulus E accordingly. But reaching the same stiffness S (and according to former investigations hence also the same tendency for buckling/crinkling) means also reaching the same resonant frequency fres again, which results in a degraded sound quality. The same applies to one who would decrease Young's modulus E and increase thickness d.
To illustrate this fact, a simple example is given. To improve sound quality an engineer reduces the thickness s of the membrane by half. Accordingly, the resonant frequency fres is also halved. Looking at the stiffness S he realizes that stiffness S is only one fourth. Hence he chooses a material having a Young's modulus E four times higher to keep the same stiffness S, but evaluating the formula for the resonant frequency fres again, he realizes that the resonant frequency fres which was halved originally is doubled and hence the same as at the start.
According to the aforesaid formulas there is no material to be expected which would lead to a breakthrough, meaning increasing sound quality (by reducing resonant frequency fres) and increasing sound pressure (by increasing stiffness S) at the same time, even when a harder material is chosen. Therefore, known materials simply have been kept, so that normally Polycarbonate (PC), Polyetherimide (PEI), Polyethylentrephthalate (PET), or Polyethylennaphtalate (PEN) have been used for membranes for example.
These materials define a technical borderline, because they only allow certain combinations of sound quality and sound pressure. Beyond this borderline buckling and/or crinkling occurs, meaning that the operating load Fo exceeds the critical buckling/crinkling load Fbc. To develop improved transducers this borderline is to be crossed.